Vortex Panel Method in Axisymmetric Cylindrical Coordinates: Inviscid Formulation

This study addresses the vortex panel method, which is an efficient solution for inviscid flow around a body. For Cartesian coordinates, the panel method has been developed and widely applied. However, a formulation has not been proposed for axisymmetric cylindrical coordinates. This study derives a Green's function corresponding to the governing equation of the potential flow in axisymmetric cylindrical coordinates by modifying the Green's function provided by Cohl and Tohline [doi:10.1086/308062]. The derived Green's function $G$ is significantly compact and is composed of a single term of the half-integer degree Legendre function of the second type. The derivation of Green's function $G$ is confirmed by analytically evaluating the requirement $ℒG=0$, where $ℒ$ is a linear operator of the governing equation. Under the derived $G$, the vortex panel method is formulated by discretizing the vorticity distribution along the body surface. The validity of the constructed panel method is confirmed through calculations of the flow past a sphere, an ellipsoid, a torus, and a teardrop-like object by comparison with analytical or numerical solutions.